Paradoxes
Created | Updated Jan 28, 2002
Paradoxes are statements that seem contrary to common sense and yet
are perhaps true. Some excelent examples of these phenomena are:
The Endless Race
A racer decides to run in a strait line from point A to point B. The paradox says he will never reach point B. Why? For this reason: if he wishes to go from point A to point B he must first cross half that distance. And in order to cross half that distance he must go half that distance- and so on Thus the runner can never go the whole distance, since he must continually cross this infinite number of half distances.
The Hangman
There is a hangman who stands on a hill along a road to town. Every person who passes is asked the same question: "Where are you going?" If the passer-by answers honestly, he or she is allowed to continue. If he or she tells a lie he or she is hanged. There is, however, one reply for which the hang man can neither hang the person or let him go. What is that reply? The answer: suppose a man comes along the road and the hangman asks him "Where are you going?" The man replies that he is coming here so that the hangman can hang him. This answer creates an irreconcilable paradox. It is unfair for the hangman to hang the traveler for the traveler has told the truth. If he lets the traveler go, however, it is also unfair, for then the traveler would have been lying.
The Martian
Lets say one day you are sitting in your back yard and a Martian spacecraft lands next to you. A martian come out and says "All Martians are liars." This cannot be true beacuse if it was the Martian was telling the truth, but if he was telling the truth he was lying. So you see it cannot be true and it cannot be a lie, for if it was a lie then it would be the truth and vice versa.
are perhaps true. Some excelent examples of these phenomena are:
The Endless Race
A racer decides to run in a strait line from point A to point B. The paradox says he will never reach point B. Why? For this reason: if he wishes to go from point A to point B he must first cross half that distance. And in order to cross half that distance he must go half that distance- and so on Thus the runner can never go the whole distance, since he must continually cross this infinite number of half distances.
The Hangman
There is a hangman who stands on a hill along a road to town. Every person who passes is asked the same question: "Where are you going?" If the passer-by answers honestly, he or she is allowed to continue. If he or she tells a lie he or she is hanged. There is, however, one reply for which the hang man can neither hang the person or let him go. What is that reply? The answer: suppose a man comes along the road and the hangman asks him "Where are you going?" The man replies that he is coming here so that the hangman can hang him. This answer creates an irreconcilable paradox. It is unfair for the hangman to hang the traveler for the traveler has told the truth. If he lets the traveler go, however, it is also unfair, for then the traveler would have been lying.
The Martian
Lets say one day you are sitting in your back yard and a Martian spacecraft lands next to you. A martian come out and says "All Martians are liars." This cannot be true beacuse if it was the Martian was telling the truth, but if he was telling the truth he was lying. So you see it cannot be true and it cannot be a lie, for if it was a lie then it would be the truth and vice versa.
